1 //===-- ConstantRange.cpp - ConstantRange implementation ------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // Represent a range of possible values that may occur when the program is run
11 // for an integral value. This keeps track of a lower and upper bound for the
12 // constant, which MAY wrap around the end of the numeric range. To do this, it
13 // keeps track of a [lower, upper) bound, which specifies an interval just like
14 // STL iterators. When used with boolean values, the following are important
15 // ranges (other integral ranges use min/max values for special range values):
17 // [F, F) = {} = Empty set
20 // [T, T) = {F, T} = Full set
22 //===----------------------------------------------------------------------===//
24 #include "llvm/InstrTypes.h"
25 #include "llvm/Support/ConstantRange.h"
26 #include "llvm/Support/Debug.h"
27 #include "llvm/Support/raw_ostream.h"
30 /// Initialize a full (the default) or empty set for the specified type.
32 ConstantRange::ConstantRange(uint32_t BitWidth, bool Full) {
34 Lower = Upper = APInt::getMaxValue(BitWidth);
36 Lower = Upper = APInt::getMinValue(BitWidth);
39 /// Initialize a range to hold the single specified value.
41 ConstantRange::ConstantRange(const APInt &V) : Lower(V), Upper(V + 1) {}
43 ConstantRange::ConstantRange(const APInt &L, const APInt &U) :
45 assert(L.getBitWidth() == U.getBitWidth() &&
46 "ConstantRange with unequal bit widths");
47 assert((L != U || (L.isMaxValue() || L.isMinValue())) &&
48 "Lower == Upper, but they aren't min or max value!");
51 ConstantRange ConstantRange::makeICmpRegion(unsigned Pred,
52 const ConstantRange &CR) {
56 uint32_t W = CR.getBitWidth();
58 default: llvm_unreachable("Invalid ICmp predicate to makeICmpRegion()");
59 case CmpInst::ICMP_EQ:
61 case CmpInst::ICMP_NE:
62 if (CR.isSingleElement())
63 return ConstantRange(CR.getUpper(), CR.getLower());
64 return ConstantRange(W);
65 case CmpInst::ICMP_ULT: {
66 APInt UMax(CR.getUnsignedMax());
67 if (UMax.isMinValue())
68 return ConstantRange(W, /* empty */ false);
69 return ConstantRange(APInt::getMinValue(W), UMax);
71 case CmpInst::ICMP_SLT: {
72 APInt SMax(CR.getSignedMax());
73 if (SMax.isMinSignedValue())
74 return ConstantRange(W, /* empty */ false);
75 return ConstantRange(APInt::getSignedMinValue(W), SMax);
77 case CmpInst::ICMP_ULE: {
78 APInt UMax(CR.getUnsignedMax());
79 if (UMax.isMaxValue())
80 return ConstantRange(W);
81 return ConstantRange(APInt::getMinValue(W), UMax + 1);
83 case CmpInst::ICMP_SLE: {
84 APInt SMax(CR.getSignedMax());
85 if (SMax.isMaxSignedValue())
86 return ConstantRange(W);
87 return ConstantRange(APInt::getSignedMinValue(W), SMax + 1);
89 case CmpInst::ICMP_UGT: {
90 APInt UMin(CR.getUnsignedMin());
91 if (UMin.isMaxValue())
92 return ConstantRange(W, /* empty */ false);
93 return ConstantRange(UMin + 1, APInt::getNullValue(W));
95 case CmpInst::ICMP_SGT: {
96 APInt SMin(CR.getSignedMin());
97 if (SMin.isMaxSignedValue())
98 return ConstantRange(W, /* empty */ false);
99 return ConstantRange(SMin + 1, APInt::getSignedMinValue(W));
101 case CmpInst::ICMP_UGE: {
102 APInt UMin(CR.getUnsignedMin());
103 if (UMin.isMinValue())
104 return ConstantRange(W);
105 return ConstantRange(UMin, APInt::getNullValue(W));
107 case CmpInst::ICMP_SGE: {
108 APInt SMin(CR.getSignedMin());
109 if (SMin.isMinSignedValue())
110 return ConstantRange(W);
111 return ConstantRange(SMin, APInt::getSignedMinValue(W));
116 /// isFullSet - Return true if this set contains all of the elements possible
117 /// for this data-type
118 bool ConstantRange::isFullSet() const {
119 return Lower == Upper && Lower.isMaxValue();
122 /// isEmptySet - Return true if this set contains no members.
124 bool ConstantRange::isEmptySet() const {
125 return Lower == Upper && Lower.isMinValue();
128 /// isWrappedSet - Return true if this set wraps around the top of the range,
129 /// for example: [100, 8)
131 bool ConstantRange::isWrappedSet() const {
132 return Lower.ugt(Upper);
135 /// isSignWrappedSet - Return true if this set wraps around the INT_MIN of
136 /// its bitwidth, for example: i8 [120, 140).
138 bool ConstantRange::isSignWrappedSet() const {
139 return contains(APInt::getSignedMaxValue(getBitWidth())) &&
140 contains(APInt::getSignedMinValue(getBitWidth()));
143 /// getSetSize - Return the number of elements in this set.
145 APInt ConstantRange::getSetSize() const {
147 return APInt(getBitWidth()+1, 0);
150 return APInt::getMaxValue(getBitWidth()).zext(getBitWidth()+1) + 1;
152 if (isWrappedSet()) {
153 APInt Result = Upper + (APInt::getMaxValue(getBitWidth()) - Lower + 1);
154 return Result.zext(getBitWidth()+1);
157 return (Upper - Lower).zext(getBitWidth()+1);
160 /// getUnsignedMax - Return the largest unsigned value contained in the
163 APInt ConstantRange::getUnsignedMax() const {
164 if (isFullSet() || isWrappedSet())
165 return APInt::getMaxValue(getBitWidth());
166 return getUpper() - 1;
169 /// getUnsignedMin - Return the smallest unsigned value contained in the
172 APInt ConstantRange::getUnsignedMin() const {
173 if (isFullSet() || (isWrappedSet() && getUpper() != 0))
174 return APInt::getMinValue(getBitWidth());
178 /// getSignedMax - Return the largest signed value contained in the
181 APInt ConstantRange::getSignedMax() const {
182 APInt SignedMax(APInt::getSignedMaxValue(getBitWidth()));
183 if (!isWrappedSet()) {
184 if (getLower().sle(getUpper() - 1))
185 return getUpper() - 1;
188 if (getLower().isNegative() == getUpper().isNegative())
190 return getUpper() - 1;
193 /// getSignedMin - Return the smallest signed value contained in the
196 APInt ConstantRange::getSignedMin() const {
197 APInt SignedMin(APInt::getSignedMinValue(getBitWidth()));
198 if (!isWrappedSet()) {
199 if (getLower().sle(getUpper() - 1))
203 if ((getUpper() - 1).slt(getLower())) {
204 if (getUpper() != SignedMin)
210 /// contains - Return true if the specified value is in the set.
212 bool ConstantRange::contains(const APInt &V) const {
217 return Lower.ule(V) && V.ult(Upper);
218 return Lower.ule(V) || V.ult(Upper);
221 /// contains - Return true if the argument is a subset of this range.
222 /// Two equal sets contain each other. The empty set contained by all other
225 bool ConstantRange::contains(const ConstantRange &Other) const {
226 if (isFullSet() || Other.isEmptySet()) return true;
227 if (isEmptySet() || Other.isFullSet()) return false;
229 if (!isWrappedSet()) {
230 if (Other.isWrappedSet())
233 return Lower.ule(Other.getLower()) && Other.getUpper().ule(Upper);
236 if (!Other.isWrappedSet())
237 return Other.getUpper().ule(Upper) ||
238 Lower.ule(Other.getLower());
240 return Other.getUpper().ule(Upper) && Lower.ule(Other.getLower());
243 /// subtract - Subtract the specified constant from the endpoints of this
245 ConstantRange ConstantRange::subtract(const APInt &Val) const {
246 assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
247 // If the set is empty or full, don't modify the endpoints.
250 return ConstantRange(Lower - Val, Upper - Val);
253 /// \brief Subtract the specified range from this range (aka relative complement
255 ConstantRange ConstantRange::difference(const ConstantRange &CR) const {
256 return intersectWith(CR.inverse());
259 /// intersectWith - Return the range that results from the intersection of this
260 /// range with another range. The resultant range is guaranteed to include all
261 /// elements contained in both input ranges, and to have the smallest possible
262 /// set size that does so. Because there may be two intersections with the
263 /// same set size, A.intersectWith(B) might not be equal to B.intersectWith(A).
264 ConstantRange ConstantRange::intersectWith(const ConstantRange &CR) const {
265 assert(getBitWidth() == CR.getBitWidth() &&
266 "ConstantRange types don't agree!");
268 // Handle common cases.
269 if ( isEmptySet() || CR.isFullSet()) return *this;
270 if (CR.isEmptySet() || isFullSet()) return CR;
272 if (!isWrappedSet() && CR.isWrappedSet())
273 return CR.intersectWith(*this);
275 if (!isWrappedSet() && !CR.isWrappedSet()) {
276 if (Lower.ult(CR.Lower)) {
277 if (Upper.ule(CR.Lower))
278 return ConstantRange(getBitWidth(), false);
280 if (Upper.ult(CR.Upper))
281 return ConstantRange(CR.Lower, Upper);
285 if (Upper.ult(CR.Upper))
288 if (Lower.ult(CR.Upper))
289 return ConstantRange(Lower, CR.Upper);
291 return ConstantRange(getBitWidth(), false);
294 if (isWrappedSet() && !CR.isWrappedSet()) {
295 if (CR.Lower.ult(Upper)) {
296 if (CR.Upper.ult(Upper))
299 if (CR.Upper.ule(Lower))
300 return ConstantRange(CR.Lower, Upper);
302 if (getSetSize().ult(CR.getSetSize()))
306 if (CR.Lower.ult(Lower)) {
307 if (CR.Upper.ule(Lower))
308 return ConstantRange(getBitWidth(), false);
310 return ConstantRange(Lower, CR.Upper);
315 if (CR.Upper.ult(Upper)) {
316 if (CR.Lower.ult(Upper)) {
317 if (getSetSize().ult(CR.getSetSize()))
322 if (CR.Lower.ult(Lower))
323 return ConstantRange(Lower, CR.Upper);
327 if (CR.Upper.ule(Lower)) {
328 if (CR.Lower.ult(Lower))
331 return ConstantRange(CR.Lower, Upper);
333 if (getSetSize().ult(CR.getSetSize()))
339 /// unionWith - Return the range that results from the union of this range with
340 /// another range. The resultant range is guaranteed to include the elements of
341 /// both sets, but may contain more. For example, [3, 9) union [12,15) is
342 /// [3, 15), which includes 9, 10, and 11, which were not included in either
345 ConstantRange ConstantRange::unionWith(const ConstantRange &CR) const {
346 assert(getBitWidth() == CR.getBitWidth() &&
347 "ConstantRange types don't agree!");
349 if ( isFullSet() || CR.isEmptySet()) return *this;
350 if (CR.isFullSet() || isEmptySet()) return CR;
352 if (!isWrappedSet() && CR.isWrappedSet()) return CR.unionWith(*this);
354 if (!isWrappedSet() && !CR.isWrappedSet()) {
355 if (CR.Upper.ult(Lower) || Upper.ult(CR.Lower)) {
356 // If the two ranges are disjoint, find the smaller gap and bridge it.
357 APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
359 return ConstantRange(Lower, CR.Upper);
360 return ConstantRange(CR.Lower, Upper);
363 APInt L = Lower, U = Upper;
366 if ((CR.Upper - 1).ugt(U - 1))
369 if (L == 0 && U == 0)
370 return ConstantRange(getBitWidth());
372 return ConstantRange(L, U);
375 if (!CR.isWrappedSet()) {
376 // ------U L----- and ------U L----- : this
378 if (CR.Upper.ule(Upper) || CR.Lower.uge(Lower))
381 // ------U L----- : this
383 if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper))
384 return ConstantRange(getBitWidth());
386 // ----U L---- : this
389 if (Upper.ule(CR.Lower) && CR.Upper.ule(Lower)) {
390 APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
392 return ConstantRange(Lower, CR.Upper);
393 return ConstantRange(CR.Lower, Upper);
396 // ----U L----- : this
398 if (Upper.ult(CR.Lower) && Lower.ult(CR.Upper))
399 return ConstantRange(CR.Lower, Upper);
401 // ------U L---- : this
403 assert(CR.Lower.ult(Upper) && CR.Upper.ult(Lower) &&
404 "ConstantRange::unionWith missed a case with one range wrapped");
405 return ConstantRange(Lower, CR.Upper);
408 // ------U L---- and ------U L---- : this
409 // -U L----------- and ------------U L : CR
410 if (CR.Lower.ule(Upper) || Lower.ule(CR.Upper))
411 return ConstantRange(getBitWidth());
413 APInt L = Lower, U = Upper;
419 return ConstantRange(L, U);
422 /// zeroExtend - Return a new range in the specified integer type, which must
423 /// be strictly larger than the current type. The returned range will
424 /// correspond to the possible range of values as if the source range had been
426 ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
427 if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
429 unsigned SrcTySize = getBitWidth();
430 assert(SrcTySize < DstTySize && "Not a value extension");
431 if (isFullSet() || isWrappedSet())
432 // Change into [0, 1 << src bit width)
433 return ConstantRange(APInt(DstTySize,0), APInt(DstTySize,1).shl(SrcTySize));
435 return ConstantRange(Lower.zext(DstTySize), Upper.zext(DstTySize));
438 /// signExtend - Return a new range in the specified integer type, which must
439 /// be strictly larger than the current type. The returned range will
440 /// correspond to the possible range of values as if the source range had been
442 ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
443 if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
445 unsigned SrcTySize = getBitWidth();
446 assert(SrcTySize < DstTySize && "Not a value extension");
447 if (isFullSet() || isSignWrappedSet()) {
448 return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
449 APInt::getLowBitsSet(DstTySize, SrcTySize-1) + 1);
452 return ConstantRange(Lower.sext(DstTySize), Upper.sext(DstTySize));
455 /// truncate - Return a new range in the specified integer type, which must be
456 /// strictly smaller than the current type. The returned range will
457 /// correspond to the possible range of values as if the source range had been
458 /// truncated to the specified type.
459 ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
460 assert(getBitWidth() > DstTySize && "Not a value truncation");
461 if (isFullSet() || getSetSize().getActiveBits() > DstTySize)
462 return ConstantRange(DstTySize, /*isFullSet=*/true);
464 return ConstantRange(Lower.trunc(DstTySize), Upper.trunc(DstTySize));
467 /// zextOrTrunc - make this range have the bit width given by \p DstTySize. The
468 /// value is zero extended, truncated, or left alone to make it that width.
469 ConstantRange ConstantRange::zextOrTrunc(uint32_t DstTySize) const {
470 unsigned SrcTySize = getBitWidth();
471 if (SrcTySize > DstTySize)
472 return truncate(DstTySize);
473 if (SrcTySize < DstTySize)
474 return zeroExtend(DstTySize);
478 /// sextOrTrunc - make this range have the bit width given by \p DstTySize. The
479 /// value is sign extended, truncated, or left alone to make it that width.
480 ConstantRange ConstantRange::sextOrTrunc(uint32_t DstTySize) const {
481 unsigned SrcTySize = getBitWidth();
482 if (SrcTySize > DstTySize)
483 return truncate(DstTySize);
484 if (SrcTySize < DstTySize)
485 return signExtend(DstTySize);
490 ConstantRange::add(const ConstantRange &Other) const {
491 if (isEmptySet() || Other.isEmptySet())
492 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
493 if (isFullSet() || Other.isFullSet())
494 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
496 APInt Spread_X = getSetSize(), Spread_Y = Other.getSetSize();
497 APInt NewLower = getLower() + Other.getLower();
498 APInt NewUpper = getUpper() + Other.getUpper() - 1;
499 if (NewLower == NewUpper)
500 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
502 ConstantRange X = ConstantRange(NewLower, NewUpper);
503 if (X.getSetSize().ult(Spread_X) || X.getSetSize().ult(Spread_Y))
504 // We've wrapped, therefore, full set.
505 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
511 ConstantRange::sub(const ConstantRange &Other) const {
512 if (isEmptySet() || Other.isEmptySet())
513 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
514 if (isFullSet() || Other.isFullSet())
515 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
517 APInt Spread_X = getSetSize(), Spread_Y = Other.getSetSize();
518 APInt NewLower = getLower() - Other.getUpper() + 1;
519 APInt NewUpper = getUpper() - Other.getLower();
520 if (NewLower == NewUpper)
521 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
523 ConstantRange X = ConstantRange(NewLower, NewUpper);
524 if (X.getSetSize().ult(Spread_X) || X.getSetSize().ult(Spread_Y))
525 // We've wrapped, therefore, full set.
526 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
532 ConstantRange::multiply(const ConstantRange &Other) const {
533 // TODO: If either operand is a single element and the multiply is known to
534 // be non-wrapping, round the result min and max value to the appropriate
535 // multiple of that element. If wrapping is possible, at least adjust the
536 // range according to the greatest power-of-two factor of the single element.
538 if (isEmptySet() || Other.isEmptySet())
539 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
540 if (isFullSet() || Other.isFullSet())
541 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
543 APInt this_min = getUnsignedMin().zext(getBitWidth() * 2);
544 APInt this_max = getUnsignedMax().zext(getBitWidth() * 2);
545 APInt Other_min = Other.getUnsignedMin().zext(getBitWidth() * 2);
546 APInt Other_max = Other.getUnsignedMax().zext(getBitWidth() * 2);
548 ConstantRange Result_zext = ConstantRange(this_min * Other_min,
549 this_max * Other_max + 1);
550 return Result_zext.truncate(getBitWidth());
554 ConstantRange::smax(const ConstantRange &Other) const {
555 // X smax Y is: range(smax(X_smin, Y_smin),
556 // smax(X_smax, Y_smax))
557 if (isEmptySet() || Other.isEmptySet())
558 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
559 APInt NewL = APIntOps::smax(getSignedMin(), Other.getSignedMin());
560 APInt NewU = APIntOps::smax(getSignedMax(), Other.getSignedMax()) + 1;
562 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
563 return ConstantRange(NewL, NewU);
567 ConstantRange::umax(const ConstantRange &Other) const {
568 // X umax Y is: range(umax(X_umin, Y_umin),
569 // umax(X_umax, Y_umax))
570 if (isEmptySet() || Other.isEmptySet())
571 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
572 APInt NewL = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
573 APInt NewU = APIntOps::umax(getUnsignedMax(), Other.getUnsignedMax()) + 1;
575 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
576 return ConstantRange(NewL, NewU);
580 ConstantRange::udiv(const ConstantRange &RHS) const {
581 if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax() == 0)
582 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
584 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
586 APInt Lower = getUnsignedMin().udiv(RHS.getUnsignedMax());
588 APInt RHS_umin = RHS.getUnsignedMin();
590 // We want the lowest value in RHS excluding zero. Usually that would be 1
591 // except for a range in the form of [X, 1) in which case it would be X.
592 if (RHS.getUpper() == 1)
593 RHS_umin = RHS.getLower();
595 RHS_umin = APInt(getBitWidth(), 1);
598 APInt Upper = getUnsignedMax().udiv(RHS_umin) + 1;
600 // If the LHS is Full and the RHS is a wrapped interval containing 1 then
603 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
605 return ConstantRange(Lower, Upper);
609 ConstantRange::binaryAnd(const ConstantRange &Other) const {
610 if (isEmptySet() || Other.isEmptySet())
611 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
613 // TODO: replace this with something less conservative
615 APInt umin = APIntOps::umin(Other.getUnsignedMax(), getUnsignedMax());
616 if (umin.isAllOnesValue())
617 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
618 return ConstantRange(APInt::getNullValue(getBitWidth()), umin + 1);
622 ConstantRange::binaryOr(const ConstantRange &Other) const {
623 if (isEmptySet() || Other.isEmptySet())
624 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
626 // TODO: replace this with something less conservative
628 APInt umax = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
629 if (umax.isMinValue())
630 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
631 return ConstantRange(umax, APInt::getNullValue(getBitWidth()));
635 ConstantRange::shl(const ConstantRange &Other) const {
636 if (isEmptySet() || Other.isEmptySet())
637 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
639 APInt min = getUnsignedMin().shl(Other.getUnsignedMin());
640 APInt max = getUnsignedMax().shl(Other.getUnsignedMax());
642 // there's no overflow!
643 APInt Zeros(getBitWidth(), getUnsignedMax().countLeadingZeros());
644 if (Zeros.ugt(Other.getUnsignedMax()))
645 return ConstantRange(min, max + 1);
647 // FIXME: implement the other tricky cases
648 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
652 ConstantRange::lshr(const ConstantRange &Other) const {
653 if (isEmptySet() || Other.isEmptySet())
654 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
656 APInt max = getUnsignedMax().lshr(Other.getUnsignedMin());
657 APInt min = getUnsignedMin().lshr(Other.getUnsignedMax());
659 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
661 return ConstantRange(min, max + 1);
664 ConstantRange ConstantRange::inverse() const {
666 return ConstantRange(getBitWidth(), /*isFullSet=*/false);
668 return ConstantRange(getBitWidth(), /*isFullSet=*/true);
669 return ConstantRange(Upper, Lower);
672 /// print - Print out the bounds to a stream...
674 void ConstantRange::print(raw_ostream &OS) const {
677 else if (isEmptySet())
680 OS << "[" << Lower << "," << Upper << ")";
683 /// dump - Allow printing from a debugger easily...
685 void ConstantRange::dump() const {